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The Celtics went for size and strength in the NBA draft, selecting Jared Sullinger and Fab Melo with the 21st and 22d picks Thursday night.

Sullinger, listed at 6 feet 9 inches, 280 pounds, played two seasons at Ohio State, declaring himself an early entry after the team’s final game, a loss to Kansas in the NCAA Tournament last season.

Melo, 7 feet, 255 pounds, was born in Juiz da Fora, Brazil, attended high school in Florida and played two seasons at Syracuse.

“Obviously, we needed to address height,” Celtics coach Doc Rivers said. “The fact that Jared Sullinger fell to us is just fortunate. Last year he would have been a top five pick. All year he was a top-10 pick. The fact that he kept falling to us gives us a rebounder, high IQ player, great passer, and a very good shooter from the outside, gives us some physical force. Fab Melo does the same thing. He has size.

“We like size, we needed size — gives us a chance to work with him. We think he can be a good player.”

Sullinger, 20, scored 1,282 points in two years with the Buckeyes. Sullinger averaged 17.2 points and 10.2 rebounds as a freshman and 17.5 points and 9.2 rebounds last season. A herniated disc, detected during a combine workout in Chicago earlier this month, likely prevented Sullinger from becoming an early selection.

“When the day started, I did not think he would be there at 21,” Celtics president of basketball operations Danny Ainge said. “We got wind, the back issues, he was slipping in the draft. He was projected much higher last week, and so we’re fortunate to get him.

“We were concerned and we did our research on him and we felt comfortable. But there are some issues there. Our medical staff thinks short term and long term there may be some maintenance issues with the back.

“Doc Rivers played with a herniated disc for 13 years. So, he may need surgery at some point and may not. All I know is what the MRI results were at the end of the combine in Chicago.”

Said Rivers: “We feel pretty good about [his back] or we wouldn’t have taken him. Obviously, we have to watch it and next year he gets the right treatment all the time. I played 13 years with a bad back and I was OK. I think he will be, too. All doctors gave clearance. When you don’t get red-flagged, you’re pretty much safe.”

Both players are expected to join Boston’s summer league teams in Orlando and Las Vegas next month.

Rivers said he is familiar with Sullinger.

“I’ve met him a couple times, couple AAU games against [my son] Austin, I think he had 30 rebounds in one game,’’ Rivers said. “I’ve met him a couple times, ironically during the NCAA Tournament, ran into his parents at Starbucks, first time I met his mom.

“Sometimes, when medical reports come out, you sit there and think, people may pass on him. I’m hoping the projections of him before the season are right, that he’s a top 10 lottery pick. I’m hoping what went on the last three weeks are wrong.”

Melo missed the end of the regular season and tournament because of an academic suspension.

“I don’t know what you can project,” Rivers said of Melo. “Obviously, he has size. We have to teach him the Celtic way, we have to teach him how to work, and understanding how to play as a winner. I love size and potential and he has both of those things. For us to get a 7-footer at that pick is a good pick for us.”

The Celtics also selected Kris Joseph with the 51st choice. Joseph, listed at 6-6, 215 pounds, averaged 13.4 points at Syracuse last season.

Ainge confirmed Boston’s attempts to move up in the draft.

“We never got to a point where teams wanted to move for what we were offering,” Ainge said. “I’m not sure how close we were. We weren’t going to sell the farm to move up in the draft.

“I liked Jared longer than his years at Ohio State. He was a dominant high school player. What I like about him is he’s complete, he can pass, he can think, he can rebound, he can shoot. And, one thing you didn’t see him do in college that I believe he can do, he can make shots, he can shoot from the perimeter. I mean, you see him do that a little bit on film, but he makes free throws and I really like his stroke. So, hopefully he can improve that part of his game because that’s an important part of our offense.

“Length is an issue. He has good width. There was a lot of these same kind of issues with Glen Davis, when he came in — you know, they just find a way, guys that are smart and have a good feel, they just make an adjustment.

“A team that is trying to win, it’s tough to count too much on three rookies coming in. So, maybe one will be ready to go, maybe two of them will be able to play a certain role. But we’ll fill in with veterans from here on out.

“I’m very optimistic for these three guys. I think they have a bright up-side. And all of them are workers, they put in the time, and want to improve and we’ll see if they can make the adjustments.”